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boneill3
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Homework Statement
Use the divergence theorem to evaluate
[itex]\int\int_{\sigma}F . n ds[/itex]
Where n is the outer unit normal to [itex]\sigma[/itex]
we have
[itex]F(x,y,z)=2x i + 2y j +2z k [/itex] and [itex]\sigma[/itex] is the sphere [itex]x^2 + y^2 +z^2=9[/itex]
Homework Equations
[itex]\int\int_{s}F . dA = \int\int\int_{R}divF dV[/itex]
The Attempt at a Solution
I've worked out [itex]divF[/itex] to be 6.
so I multyiply that by the Volume of a sphere [itex]6\times\frac{4}{3}\pi r^3 = 216\pi[/itex]
To calulate this using spherical co-ordinates.
I would need to calculate a triple integral
I know there's
[itex]\int\int\int p^2 sin(\theta) dp d\theta d\phi[/itex]
I know that p = 3 but what would the values of [itex]\theta [/itex] and [itex]\phi [/itex] be
I guess the limits would be [itex]0<p<3[/itex][itex] 0<\phi<2pi[/itex] and [itex]0<\theta<\phi[/itex]
Any help greatly appreciated
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